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Feedback-polynomial parity condition for maximal period

A maximal-period feedback polynomial cannot have

1

as a root. Over

F_{2}

, this says

1 + a_{d - 1} + \dots + a_{0} \neq = 0,

so an even number of the coefficients

a_{i}

equal one and the full monic polynomial has an odd number of nonzero coefficients.

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Solution